# Recommended root canal

Algebra Level 4

Find the largest possible product $n\cdot m$ of two distinct positive integers $n$ and $m,$ such that the equations $(x+1)^n=x^n+1$ and $(x+1)^m=x^m+1$ have the same set of complex roots.

Details and assumptions

The multiplicities of the roots can, of course, be different, but each root of one equation is a root of the other.

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